Physical Sciences and Mathematics Commons^™

Using Random Forests To Estimate Win Probability Before Each Play Of An Nfl Game, Dennis Lock, Dan Nettleton

Dan Nettleton

Before any play of a National Football League (NFL) game, the probability that a given team will win depends on many situational variables (such as time remaining, yards to go for a first down, field position and current score) as well as the relative quality of the two teams as quantified by the Las Vegas point spread. We use a random forest method to combine pre-play variables to estimate Win Probability (WP) before any play of an NFL game. When a subset of NFL play-by-play data for the 12 seasons from 2001 to 2012 is used as a training dataset, …

Surprise Vs. Probability As A Metric For Proof, Edward K. Cheng, Matthew Ginther

Edward Cheng

In this Symposium issue celebrating his career, Professor Michael Risinger in Leveraging Surprise proposes using "the fundamental emotion of surprise" as a way of measuring belief for purposes of legal proof. More specifically, Professor Risinger argues that we should not conceive of the burden of proof in terms of probabilities such as 51%, 95%, or even "beyond a reasonable doubt." Rather, the legal system should reference the threshold using "words of estimative surprise" -asking jurors how surprised they would be if the fact in question were not true. Toward this goal (and being averse to cardinality), he suggests categories such …

Excess Versions Of The Minkowski And Hölder Inequalities, Iosif Pinelis

Iosif Pinelis

No abstract provided.

Some Applications Of Sophisticated Mathematics To Randomized Computing, Ronald I. Greenberg

Ronald Greenberg

No abstract provided.

Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg

Ronald Greenberg

Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.

Propagating Lyapunov Functions To Prove Noise-Induced Stabilization, Tiffany Kolba, Avanti Athreya, Jonathan Mattingly

Tiffany N Kolba

No abstract provided.

Estimated Probability Of Becoming A Case Of Drug Dependence In Relation To Duration Of Drug-Taking Experience: A Function Approach, Olga A. Vsevolozhskaya, James C. Anthony

Olga A. Vsevolozhskaya

Measured as elapsed time from first use to dependence syndrome onset, the estimated 'induction interval' for cocaine clearly is short relative to the cannabis interval, but little is known about risk of becoming dependent when use persists. Published estimates for this facet of drug dependence epidemiology are from life histories elicited years after first use. To improve estimation, we turn to new data from nationally representative samples of newly incident drug users identified via probability sampling and confidential computer-assisted self-interviews for the National Surveys on Drug Use and Health, 2004-2013. Standardized modules assess first and most recent use, and dependence …

Assessing The Probability That A Finding Is Genuine For Large-Scale Genetic Association Studies, Chia-Ling Kuo, Olga A. Vsevolozhskaya, Dmitri V. Zaykin

Olga A. Vsevolozhskaya

Genetic association studies routinely involve massive numbers of statistical tests accompanied by P-values. Whole genome sequencing technologies increased the potential number of tested variants to tens of millions. The more tests are performed, the smaller P-value is required to be deemed significant. However, a small P-value is not equivalent to small chances of a spurious finding and significance thresholds may fail to serve as efficient filters against false results. While the Bayesian approach can provide a direct assessment of the probability that a finding is spurious, its adoption in association studies has been slow, due in part to the ubiquity …

Probabilistic Analysis Of The Economic Impact Of Earthquake Prediction Systems, Tiffany Kolba, Ruyue Yuan

Tiffany N Kolba

Probabilities In Probable Cause And Beyond: Statistical Versus Concrete Harms, Sherry F. Colb

Sherry Colb

No abstract provided.

An Inspiration From San Diego, Gabriel Leiner

Gabriel Leiner

The city of San Diego is the only place in America that maintains a public transportation system designed to run in a circle, which is a shape with a common start and end point. The point of this paper is to model these types of systems. The code for the model constructed here is in the D programming language and uses constraints and equations to simulate trial runs of trains along a track. Trains move as objects and make station stops at nodes. The model uses a random number generator to simulate boarding times and allows vehicles to coast around …

A General Framework For Uncertainty Propagation Based On Point Estimate Methods, René Schenkendorf

René Schenkendorf

A general framework to approach the challenge of uncertainty propagation in model based prognostics is presented in this work. It is shown how the so-called Point Estimate Meth- ods (PEMs) are ideally suited for this purpose because of the following reasons: 1) A credible propagation and represen- tation of Gaussian (normally distributed) uncertainty can be done with a minimum of computational effort for non-linear applications. 2) Also non-Gaussian uncertainties can be prop- agated by evaluating suitable transfer functions inherently. 3) Confidence intervals of simulation results can be derived which do not have to be symmetrically distributed around the mean value …

Use Of P-Values To Evaluate The Probability Of A Genuine Finding In Large-Scale Genetic Association Studies, Olga A. Vsevolozhskaya, Qing Lu, Chia-Ling Kuo, Dmitri V. Zaykin

Olga A. Vsevolozhskaya

To claim the existence of an association in modern genome-wide association studies (GWAS), a nominal P-value has to exceed a stringent Bonferroni-adjusted significance level. Despite strictness of the correction, a significant P-value does not indicate high probability that the claimed association is genuine. A simple Bayesian solution -- the False Positive Report Probability (FPRP) -- was previously proposed to convert the observed P-value to the corresponding probability of no true association. Although the FPRP solution is highly popular, it does not reflect probability that a particular finding is false. Here, we offer a simple POFIG method -- a Probability that …

Introduction Aux Méthodes D’Intégrale De Chemin Et Applications, Nour-Eddiine Fahssi

Nour-Eddine Fahssi

These lecture notes are based on a master course given at University Hassan II - Agdal in spring 2012.

The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell

Byron E. Bell

Estimation Of P[Y X] For Generalized Pareto Distribution, Manijeh Mahmoodi, Sadegh Rezaei, Rasool Tahmasbi

manijeh mahmoodi

No abstract provided.

The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell

Byron E. Bell

No abstract provided.

Masw Tests For Detection Of Decayed Buried Timber Within Railway Embankments, Barry A. Palynchuk Phd, Chris Bunce Phd, Steve Sather M.Eng

Barry A. Palynchuk PhD

No abstract provided.

Approaches To Mitigating Decayed Buried Timber Within Railway Embankments, Barry A. Palynchuk Phd

Barry A. Palynchuk PhD

During the last three years, several sinkholes have been observed along CPR railway lines in Southern Ontario. The sinkholes have formed as a result of the decay of buried timber trestles in railway embankments. Although it has not occurred the sinkholes could result in hazardous changes in track geometry under load. This study summarizes the site investigation results and remedial methods implemented at five sites in southern Ontario. Remedial methods include placement geosynthetic reinforcement, soil-cement column reinforcement and grouting of voids at the trestle bents. The design, installation methods and construction constraints for the remedial options are described in this …

A Mathematical Regression Of The U.S. Gross Private Domestic Investment 1959-2001, Byron E. Bell

Byron E. Bell

SUMMARY OF PROJECT What did I do? A study of the role the U.S. stock markets and money markets have possibly played in the Gross Private Domestic Investment (GPDI) of the United States from the year 1959 to the year 2001 and I created a Multiple Linear Regression Model (MLRM).

Comparison Between Analytical Probabilistic And Computer Simulation Models, Using Current Design Examples, Barry A. Palynchuk Phd

Barry A. Palynchuk PhD

Closed form analytical expressions have been developed to solve several basic problems related to the hydrologic design of storm water management facilities. The collection of these analytical expressions is referred to as the Analytical Probabilistic Storm Water Models (APSWM). APSWM can be used as an alternative to the design storm simulation models in the design and analysis of storm water management facilities. In this paper, a comparison is made between APSWM and design storm simulation models as applied to an actual design case. Conventional outputs such as runoff volume, peak discharge, and peak discharge from detention ponds are reviewed and …

Emergency Response Canadian Pacific Railway Canadian Main Line, Barry A. Palynchuk Phd, Michael J. Loehr, Robert W. Badger, Robert P. Conroy, Clive H. Mackay

Barry A. Palynchuk PhD

In late June 1998, a major storm event occurred in the Adirondack Mountains in the vicinity of Keeseville, New York about 150 miles north of Albany. This storm resulted in unprecedented damage to the Canadian Pacific Railway (CPR) Canadian Mainline along the shores of Lake Champlain. The storm caused 14 major embankment failures and washouts, numerous minor failures, severe bridge foundation scour and a major mainline derailment.